Israeli Merkava tanks roll at an army deployment near Israel's border with the Gaza Strip on July 20, 2014. / Jack Guez, AFP/Getty Images

by Michele Chabin, Special for USA TODAY

by Michele Chabin, Special for USA TODAY

JERUSALEM - At 4:30 a.m. Thursday, Hadas Gronshpan was awakened by a cellphone alert from the Israel Defense Forces.

"We learned there might be an intrusion from Gaza and were told to stay in our homes and lock the doors," Gronshpan, a member of the emergency response team at the Sufa kibbutz - a communal farm - recalled from her house located less than 1.5 miles from the Gaza border.

A half hour later the electricity went out.

"We stayed in our safe rooms, sat in the dark and waited," Gronshpan said, referring to the bomb shelters attached to every home on the kibbutzim in the area, which has been the target of Gaza rocket fire for nearly 15 years.

When the all-clear came, with the news that the Israeli military had intercepted an armed 13-member Hamas "terror" squad close to the kibbutz, it did little to calm her fears.

"Imagine if someone was entering your house from under the ground. A safe room won't protect us from that. When it comes to these tunnels, nowhere is safe."

Israel says the main goal of its ground operation in Gaza, launched hours after the Sufa incident, is to find and destroy the vast web of underground tunnels Hamas and other militants use to smuggle and hide weapons and fighters.

The tunnels that furrow below the Gaza-Israeli border represent the biggest threat, the Israeli military says.

Those tunnels "provide a direct channel for terrorists from Gaza to commit potential acts of mass terror," said Lt. Libby Weiss, an IDF spokeswoman, who added that Hamas has invested "significant" resources in building them.

"These are sophisticated tunnels, made of cement, and stretch for quite a distance," she said, adding they can originate in civilian or open areas.

Since the start of the ground operation late Thursday night, the Israeli military has uncovered dozens of shafts and openings leading into more than a dozen underground tunnels, Weiss said.

Even as Israeli forces bear down on them, Hamas militants are still attempting to infiltrate Israel using cross-border tunnels. On Saturday, Palestinian gunmen disguised in Israeli uniforms crossed into Israel a couple of miles from two kibbutzim. At least one Palestinian and two Israeli soldiers were killed, the Israeli military said.

Israel, which sends warnings to Palestinian civilians to flee their neighborhoods in advance of military action, announced Sunday it would erect a field hospital for injured Palestinians on the Israeli side of the Erez border crossing.

Palestinians say the warnings are often useless because the ground operation targets many neighborhoods, and Gaza has few bomb shelters.

Shimon Daniel, a retired brigadier general and former head of the Israeli military's engineer corps, said the military knew Hamas had a large number of tunnels designed to assault Israel.

"I think finding (so many) tunnels in such a short time is a great achievement," he told Channel 10 TV.

He said demolishing the tunnels is dangerous. Troops must assume the passages are booby trapped. Soldiers first close off the area and check for additional openings. Then robots go inside to look around, he said.

Ayalon, co-founder of Blue White Future, an organization that advocates for a Palestinian state living alongside Israel, said that while Israel must destroy the tunnels because they are being used as launching pads for terror attacks, it won't solve the problem.

"The only solution is to create a political atmosphere in which most people on both sides believe we are heading to a two-state reality. This isn't Hamas' dream," he acknowledged, "but it's the dream of most Palestinians."

Gronshpan said that for a two-state solution to be realized the people of Gaza will first need to force Hamas out of power.

"My heart aches for the Palestinian casualties but as long as Hamas is their chosen leadership and there are tunnels that run under the Israeli border, the people of Gaza are Hamas followers," she said. "When I see them demonstrating in the streets against Hamas, I can say they are looking for change."